# 8.3: Definition of Reaction Rate

If one assumes that the batch reactor shown in Figure $$8.2.1$$ is perfectly mixed, Equation ($$8.2.4$$) takes the form

$\frac{dc_{A} }{dt} =R_{A} ,\left\{\begin{array}{c} \text{perfectly mixed,} \\ \text{constant volume} \\ \text{ batch reactor} \end{array}\right\} \label{34}$

Often there is a tendency to think of this result as defining4 the “reaction rate” and this is a perspective that one must avoid. Equation \ref{34} represents a special form of the macroscopic mole balance for species $$A$$ and it does not represent a definition of $$R_{A}$$. In reality, Equation \ref{34} represents a very attractive special case that can be used with laboratory measurements to determine the net molar rate of production of species $$A$$, $$R_{A}$$. Once $$R_{A}$$ has been determined experimentally, one can search for chemical kinetic rate expressions such as that given by Eq. ($$8.2.9$$), and details of that search procedure are described in Chapter 9. If successful, this search provides both a satisfactory form of the rate expression and it provides reliable values of the parameters that appear in the rate expression. To be convinced that Equation \ref{34} is not a definition of the reaction rate, one need only consider the perfectly mixed version of Equation ($$8.2.3$$) which is given by

$\frac{dc_{A} }{dt} + \frac{c_{A} }{\mathscr{V}(t)} \frac{d\mathscr{V}(t)}{dt} =R_{A} ,\left\{\begin{array}{c} \text{perfectly mixed,} \\ \text{ batch reactor} \end{array}\right\} \label{35}$

Here it should be clear that $$R_{A}$$ is not defined by $$dc_{A} /dt$$; rather $$R_{A}$$ is an intrinsic property of the system that represents the net molar rate of production of species $$A$$ per unit volume. This is the sense in which the rate of production was introduced in Chapter 4.